Abstract Flow velocity controls hillslope soil erosion and is a key hydrodynamic variable involved in sediment transport and deposition processes. The dye-tracer technique is one of the most applied methods for measuring velocity of shallow interrill and rill flow. The technique is based on the injection of a tracer in a specific point and the measurement of its speed to travel the known distance from the injection point to a given channel section. The dye-tracer technique requires that the measured surface flow velocity has to be corrected to obtain the mean flow velocity using a correction factor which is generally empirically deduced. The technique has two sources of uncertainties: i) the method applied for measuring the travel time of the dye-tracer and ii) the estimate of the correction factor, which is the ratio between the mean flow velocity and the surface velocity, in different flow conditions. In this paper the results of a wide experimental investigation, carried out using a fixed bed small flume simulating a rill channel, are presented. At first, the comparison between a chronometer-based (CB) and video-based (VB) technique was carried out for establishing the influence of the travel time measuring technique. For each experimental run, which was characterized by a sample of 20 measurements carried out with the same values of slope and discharge, the developed analysis showed that the empirical frequency distribution of the ratio between the single measurement and the sample mean (i.e., the average of 20 measurements) is more uniform for the VB technique than for the CB one. In any case, this sample mean was representative of surface flow velocity for both the CB and the VB technique. Furthermore, the mean value obtained by the CB measurements lightly underestimated (−1.7%) the corresponding mean obtained by the VB technique. Finally, the effects of slope (0.1–8.7%), flow Reynolds number (3462–10040), Froude number (1.44–5.17) on the correction factor are presented. The analysis demonstrated that the correction factor is independent of flow Reynolds number while a relationship with a Froude number, obtained by surface velocity measurement, or channel slope can be established.

中文翻译：

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用于评估细流中染料示踪技术的水槽实验

摘要 流速控制山坡土壤侵蚀，是参与泥沙输送和沉积过程的关键水动力变量。染料示踪技术是测量浅层间细沟和细沟流速度应用最广泛的方法之一。该技术基于在特定点注入示踪剂并测量其从注入点行进已知距离到给定通道部分的速度。染料示踪技术要求必须使用通常凭经验推导出的校正因子来校正测量的表面流速以获得平均流速。该技术有两个不确定性来源：i) 用于测量染料示踪剂传播时间的方法和 ii) 校正因子的估计，它是不同流动条件下平均流速与表面速度的比值。在本文中，介绍了使用模拟细沟的固定床小水槽进行的广泛实验研究的结果。首先，进行了基于天文台 (CB) 和基于视频 (VB) 的技术之间的比较，以确定走时测量技术的影响。对于每个实验运行，其特征在于以相同的斜率和流量值进行 20 次测量的样本，开发的分析表明，单次测量与样本平均值（即平均值）之间的比率的经验频率分布20 次测量）对于 VB 技术比对于 CB 技术更一致。任何状况之下，该样本平均值代表了 CB 和 VB 技术的表面流速。此外，通过 CB 测量获得的平均值略微低估 (-1.7%) 通过 VB 技术获得的相应平均值。最后，介绍了斜率 (0.1–8.7%)、流量雷诺数 (3462–10040)、弗劳德数 (1.44–5.17) 对校正因子的影响。分析表明，校正因子与流量雷诺数无关，而与通过表面速度测量获得的弗劳德数或通道坡度的关系可以建立。流量雷诺数 (3462–10040)、弗劳德数 (1.44–5.17) 关于修正因子。分析表明，校正因子与流量雷诺数无关，而与通过表面速度测量获得的弗劳德数或通道坡度的关系可以建立。流量雷诺数 (3462–10040)、弗劳德数 (1.44–5.17) 关于修正因子。分析表明，校正因子与流量雷诺数无关，而与通过表面速度测量获得的弗劳德数或通道坡度的关系可以建立。